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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="metric_1.html#V1">strict</a> <a href="metric_1.html#NM1">MetrSpace</a>;<br/>

<a NAME="E1:4"/><i><font color="Green">E4</font></i>: 
the <a href="metric_1.html#U1">distance</a> of <font color="Maroon">c<sub>1</sub></font> <a href="pcomps_1.html#R1">is_metric_of</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="pcomps_1.html#T39">PCOMPS_1:39</a></i>;<br/>
<b>hence </b><a NAME="E2:4"/>
the <a href="metric_1.html#U1">distance</a> of <font color="Maroon">c<sub>1</sub></font> is <a href="metric_1.html#V2">Reflexive</a>
 <b>by </b><i><a class="ref" href="metric_6.html#T3" target="_self">Th3</a></i>;<br/>

<b>thus </b><a NAME="E3:4"/>
the <a href="metric_1.html#U1">distance</a> of <font color="Maroon">c<sub>1</sub></font> is <a href="metric_1.html#V3">discerning</a>
 <b>by </b><i><a class="txt" href="metric_6.html#E1:4"><i><font color="Green">E4</font></i></a>, <a class="ref" href="metric_6.html#T3" target="_self">Th3</a></i>;<br/>

<b>thus </b><a NAME="E4:4"/>
the <a href="metric_1.html#U1">distance</a> of <font color="Maroon">c<sub>1</sub></font> is <a href="metric_1.html#V4">symmetric</a>
 <b>by </b><i><a class="txt" href="metric_6.html#E1:4"><i><font color="Green">E4</font></i></a>, <a class="ref" href="metric_6.html#T3" target="_self">Th3</a></i>;<br/>

<b>thus </b><a NAME="E5:4"/>
the <a href="metric_1.html#U1">distance</a> of <font color="Maroon">c<sub>1</sub></font> is <a href="metric_1.html#V5">triangle</a>
 <b>by </b><i><a class="txt" href="metric_6.html#E1:4"><i><font color="Green">E4</font></i></a>, <a class="ref" href="metric_6.html#T3" target="_self">Th3</a></i>;<br/>


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